Calculating Whole Circle Bearing

The Whole Circle Bearing (WCB) represents the angle measured clockwise from the North direction to the line.

We are given the components of the line:

• Departure = 70 m (Eastward component)
• Latitude = -130 m (Southward component)

Determining the Line's Quadrant

A positive departure indicates the line moves East. A negative latitude indicates the line moves South. Therefore, the line lies in the Southeast (SE) quadrant.

Calculating the Reference Angle

First, calculate the acute angle ($\alpha$) the line makes with the North-South meridian using the absolute values of departure (D) and latitude (L).

The formula is:

$\tan(\alpha) = \frac{| \text{Departure} |}{| \text{Latitude} |}$

Substitute the given values:

$\tan(\alpha) = \frac{70}{130} \approx 0.53846$

Find the angle $\alpha$:

$\alpha = \arctan\left(\frac{70}{130}\right) \approx 28.299^\circ$

Finding the Whole Circle Bearing (WCB)

For lines in the Southeast quadrant, the WCB is calculated relative to the North direction.

The angle from North clockwise to South is $180^\circ$. The reference angle $\alpha$ calculated is the angle Eastward from the South meridian.

The WCB formula for the SE quadrant is:

$WCB = 180^\circ - \alpha$

Substitute the calculated $\alpha$:

$WCB = 180^\circ - 28.299^\circ \approx 151.701^\circ$

Rounding to the nearest degree, the Whole Circle Bearing is 152 degrees.